Thermal energy storage by means of an absorption cycle

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THERMAL ENERGY STORAGE

BY MEANS OF

AN ABSORPTION CYCLE

Proefschrift

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus,

prof.dr. J.M. Dirken

in het openbaar te verdedigen

ten overstaan van een commissie

door het College van Dekanen daartoe aangewezen, op

dinsdag 6 oktober 1987 om 16.00 uur

door

JOHANNES PETRUS RUITER

geboren te Diemen

werktuigkundig ingenieur

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Dit proefschrift is goedgekeurd door de promotor PROF. IR. A.L. STOLK

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ACKNOWLEDGEMENTS

The investigation desaibed here was executed at the central research laboratories of the Dutch electric utilities (N.V. KEMA, Arnhem). I wish to thank the management for enabling me to write this thesis. I want to express my gratitude to everyone who participated in this project for her or his enthusiastic cooperation.

I also acknowledge prof. ir. A.L. Stolk for his advice and support.

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10 REFERENCES 143

NOMENCLATURE 145

APPENDIX: WORKING PAIRS 149

CURRICULUM VITAE 159

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ABSTRACT

A great part of the thermal energy that is now wasted could be used for space heating or industrial process heat provided that this heat could be stored with sufficiently high efficiency. Fossil fuels could be saved and renewable energy sources could be better utilized.

In this thesis, the investigation is described of the possibilities for storing thermal energy by means of an absorption cycle. In such a cycle two components of a mixture are separated by the supply of energy (heat or mechanical energy). The components can be stored at ambient temperature; consequently there is no heat loss during storage. At the moment of heat demand, both components are recombined to produce heat of absorption. This heat consists of the heat of mixing and the heat of condensation, provided that one of the components is gaseous. The required heat of evaporation is extracted from the environment. The energetic efficiency of such a cycle, related to the net heat production and the supplied primary energy, can theoretically be over 100%.

The absorption cycle was investigated for three different storage alternatives. In the first alternative the components are separated by supply of heat. The heat of condensation of the gaseous component is transferred to the environment. The energetic efficiency of this cycle is less than 100%. In the second storage alternative the heat of desorption is supplied by a heat pump that uses the heat of condensation as a heat source. In the third alternative the heat of condensation is produced at such a high temperature that this heat can be used directly for the desorption. To achieve this higher temperature, the gaseous component is condensed at a higher pressure. A compressor is applied for this purpose.

A simplified thermodynamic description of mixtures and solutions was derived that allows the investigation of various working pairs for the absorption cycle. By this method, the excess values of a real mixture (with respect to an ideal one) can be described by eleven working-pair coefficients. The accuracy is sufficient to allow a selection out of various potential mixtures or solutions and to calculate the design parameters for an installation.

A model was developed for the absorption cycle with the above mentioned three alternatives, by means of which eighteen different working pairs were investigated. This model was based on realistic assumptions and the outcome showed that the volumetric energy density of an absorption cycle with NH3/H20 as a working pair is more than twice that of heat storage in water, despite the separate

storage of both components. Furthermore, it appears from the calculations that a cycle with the third storage alternative (compressor) is generally more favourable than one with the second alternative (heat pump). The calculated energetic efficiency of a cycle with the first storage alternative is 68% and that of a cycle with the third alternative is 94%, based on primary energy.

The model was verified for cycles with the first and third storage alternatives, for a mixture (NH3/H20) as well as for a solution (NH3/NaSCN). An experimental installation was built for the

purpose, with a net heat output of 5 kW and a storage capacity of 40 kWh. The experimental results agree within 9% with the values that were calculated from the model.

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SAMENVATTING

Veel van de thermische energie die nu verloren gaat, zou kunnen worden gebruikt voor ruimteverwar ming of voor proceswarmte in de industrie indien warmte zou kunnen worden opgeslagen met een voldoende hoog rendement. Hierdoor zouden fossiele brandstoffen bespaard kunnen worden en zouden andere bronnen beter kunnen worden benut.

In dit proefschrift wordt het onderzoek beschreven naar de mogelijkheden van warmte-opslag door middel van een absorptiecyclus. Hierbij worden door energietoevoer (warmte of mechanische energie) twee componenten van een mengsel gescheiden. De componenten kunnen bij omgevingstemperatuur worden opgeslagen; er treedt dus geen warmteverlies op tijdens de opslag. Op het moment van de warmtevraag worden beide componenten weer bij elkaar gebracht, waarbij de absorptiewarmte vrijkomt. Indien één van beide componenten gasvormig is, bestaat de warmteproduktie zowel uit de mengwarmte als uit de condensatiewarmte. De benodigde verdampingswarmte wordt hierbij aan de omgeving onttrokken. Het energetisch rendement van een dergelijke cyclus, betrokken op de netto geleverde warmte en de toegevoerde primaire energie, kan theoretisch hoger zijn dan 100%.

De absorptiecyclus is onderzocht voor drie verschillende opslagvarianten. In variant 1 worden de componenten gescheiden door het toevoeren van warmte. De condensatiewarmte van de gasvormige component wordt afgevoerd naar de omgeving. Het energetisch rendement van deze cyclus is lager dan 100%. In opslagvariant 2 wordt de desorptiewarmte geleverd door een warmtepomp die als warmte bron de condensatiewarmte benut. In variant 3 wordt de condensatiewarmte bij een zo hoge temperatuur geproduceerd dat deze rechtstreeks kan worden gebruikt als desorptiewarmte. Om deze hogere temperatuur te bereiken, dient de condensatie bij hogere druk te geschieden. Hiertoe wordt een compressor toegepast.

Om verschillende stoffenparen voor de absorptiecyclus te kunnen onderzoeken is een vereenvou digde thermodynamische beschrijving van mengsels en oplossingen opgesteld. Hiermee kunnen door elf stoffenpaar-afhankelijke coëfficiënten de exces-waarden van een reëel mengsel t.o.v. een ideaal mengsel worden beschreven, met een nauwkeurigheid die voldoende is om een selectie uit verschil lende potentieel toepasbare mengsels of oplossingen te kunnen maken en om de ontwerpgegevens voor een installatie te kunnen berekenen.

Voor de absorptiecycli met de drie eerder genoemde varianten is een model opgesteld, waarmee achttien verschillende stoffenparen zijn onderzocht. Uitgaande van realistische aannamen is met dit model berekend dat de volumetrische energiedichtheid van een absorptiecyclus met NH3/H20 als

stoffenpaar, ondanks de gescheiden opslag van beide componenten, meer dan tweemaal zo hoog is als van warmte-opslag in water. Voorts blijkt uit de berekeningen dat een cyclus met opslagvariant 3 (compressor) in het algemeen gunstiger is dan met variant 2 (warmtepomp). Het berekende energe tische rendement van een cyclus met opslagvariant 1 bedraagt 68% en van een cyclus met variant 3 is het energetische rendement 94%, betrokken op primaire energie.

Het model is geverifieerd voor cycli met opslagvariant 1 en 3, zowel voor een mengsel (NH3/H20)

als voor een oplossing (NH3/NaSCN). Hiertoe is een experimentele installatie gebouwd met een netto

warmteproduktie van 5 kW en een opslagcapaciteit van 40 kWh. De experimentele resultaten komen binnen 9% overeen met de uit het model berekende waarden.

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1 INTRODUCTION

1.1 GENERAL

Space heating is one of the most important energy consumers in moderate and colder climates. This heating, like a significant part of industrial process heat, requires low-grade energy (temperature < 100 °C). However, the demand is at present mainly met by the high-grade combustion heat of fossil fuels.

A problem with respect to the application of sources that supply low-temperature heat is that heat output and heat demand are not always in phase. Intermittent low-temperature heat sources include solar collectors and industrial residual heat. District heating, as a by-product of electricity generation, is also a low-temperature heat source. In these cases, as well as in other systems for cogeneration of heat and electricity, storage of thermal energy can increase the implementation of low-temperature heat sources, thus saving fossil fuels.

Another option is to store other forms of energy instead of heat so as to produce heat at the moment of demand. Relatively cheap electricity can then be used during off-peak hours (e.g. at night) to produce heat in the daytime. This could be a load-management instrument to enable the utilities to fill the night dip in electricity production, resulting in an increase of the average electricity generating efficiency and consequently also in energy conservation.

These possible energy savings have aroused increasing interest in the storage of thermal energy, as is apparent from literature (Beckmann & Gilli, 1983; NTIS, 1985) as well as from symposia (SCBR,

1983).

1.2 CLASSIFICATION OF THERMAL STORAGE SYSTEMS

1.2.1. Application

Heat-storage systems can be classified on the basis of their application according to the following aspects:

- demand: space or process heat, - term: long or short (season or hours),

- heat output: large or small (of the order of kW or MW).

The demand for space heating depends on the climate and the season. In moderate climates, the irradiated solar energy during the summer, if it could be stored over a season, could meet the heat demand in the winter. The heat output of such a system should be in the order of kW for one dwelling or in the order of MW for a district. Short-term (hours) as well as long-term (months) storage could be of importance for district-heating systems that distribute the cogenerated heat of a power plant.

The temperature of the space heating depends on the type of indoor heat distribution. The temperature required for a conventional hydronic system with radiators is about 90 °C. The temperature required for a floor-heating system is only about 35 °C.

Heat for industrial processes can be stored toward peaking of the demand. Heat storage can be even more advantageous for batch-wise operated processes. This type of storage is usually a short-term one (hours or days). The temperature range of this demand is wider than that for space heating.

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1.2.2 Types of thermal storage

1.2.2.1 Sensible heat

Systems that store sensible heat make use of a storage medium with a high heat capacity e.g. water or soil. The storage system can be relatively uncomplicated. A disadvantage of this type is the temperature decrease on discharge of the system. If a temperature difference of 30 K is allowed, the energy density of water is 126 kJ.kg-1. In order to keep the heat leakage out of the storage system to the ambient

acceptably low over a season, the volume/surface ratio has to be high. This type of storage can then only be economic if applied on a large scale. Such systems exist in The Netherlands, e.g. in Groningen (TPD, 1983), and in Bunnik (Crooymans & Groeneveld, 1985). In Groningen, part of the annual heat demand for 96 dwellings is supplied (at 43 °C) by a seasonal storage system in which solar heat is stored in the soil during the summer. In Bunnik, solar heat and the surplus heat of air-conditioning and computer-cooling systems are stored for one season in subsurface water-bearing sand layers (aquifers). Also, there is a Dutch national programme (PBE, 1985) for investigation of the possibilities of thermal-energy storage in aquifers.

An example of short-term systems in which sensible heat is stored on a large scale is the storage system incorporated in the district heating of Rotterdam, Roca (Hoogendoorn, 1985; GEBR, undated). Examples of short-term storage systems on a small scale are oil-filled electric heaters that consume cheap electricity during off-peak hours.

1.2.2.2 Latent heat

Latent-heat storage systems are based on the heat associated with phase changing. This type of heat represents much more energy than the sensible heat. Another advantage of storing latent heat is the nearly isothermal charge and discharge.

For water, the heat of vaporization at atmospheric pressure and at 100 °C is 2257 kJ.kg-1, compared

to 126 kJ.kg-1, or 122 MJ.nr3 for sensible heat, at a temperature difference of 30 K. However, the

volume of steam to be stored is increased by a factor of 1600 with respect to the volume of water. The energy density per volume due to the latent heat is thus only 1.35 MJ.nr3.

Other materials (such as hydrated salts) with a phase change at lower temperatures are used in small, short-term storage systems (Anonymous, 1984). Glauber's salt (Na2SO4.10H2O) is an example of such

a medium with a heat of transition of 253 kJ.kg-1 at 32 °C. The storage capacity of hydrated salts may,

however, decrease upon cycling because the anhydrous solids that are formed during charging do not rehydrate completely on discharging (Young, 1982). Subcooling of the liquid before solidifying, can also be a problem causing a temperature decrease of the heat output (Hoogendoorn, 1985). Moreover, heat extraction from solid materials may require special types of constructions.

1.2.2.3 Physico-chemical reaction heat

In storage systems that are based on bond energy, the energy to be stored is used for the separation of two components (A and B) that are physically and/or chemically bound. The separation, or heterogeneous vaporization as Alefeld (1975a,b) called it, is represented by the reaction scheme:

discharge

AB (liquid or solid) + energy % A (liquid or solid) + B (gaseous) charge

Heat is formed in the discharge mode by recombination of the two components. If one component is a gas, the recombination heat consists of the heat of condensation and of mixing so that the energy density per unit mass is high. However, the two components have to be stored separately in such systems and this decreases the energy density per volume and makes the system more complex than those based on

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sensible or latent heat. Moreover, the driving force required for the recombination causes subcooling of the components and thus a decrease in temperature of the heat output. This subcooling, however, is much less than that mentioned for the hydrated salts (section 1.2.2.2).

Physical binding is, for instance, the adsorption of water vapour on zeolites (cristalline alumino silicates) as described by Alefeld (1981) and Maier-Laxhuber (1985). Another type of binding can be formed by a reversible reaction by which a gas is absorbed into a solid or liquid absorbent. If a chemical reaction with a solid absorbent is used, such as mentioned by Plank (1959):

CaCl2.8NH3(s) + heat ^ CaCl2.4NH3(s) + 4NH3(g)

the exchange of heat is more difficult than with a liquid absorbent. Moreover, the mole fraction of the absorbate (in absorption cycles also indicated by the term 'refrigerant') is a fixed one with respect to the solid absorbent. If a liquid mixture or solution is applied as an absorbent, the mole fraction constitutes another degree of freedom, enabling optimization of the storage system (see section 2.3). Furthermore, if a liquid absorbent is used instead of a solid one, the cooling losses between the charge and discharge mode can be lessened more easily by means of internal heat exchange. An example of such a reaction is the absorption of gaseous ammonia into a liquid mixture of ammonia and water.

1.3 SCOPE OF THIS STUDY

The aim of this study was the investigation of an absorption cycle for short-term storage of thermal energy on a medium scale, i.e. for one building or a block of dwellings. The heat is to be supplied at a low temperature suitable for a heat distribution system consisting of radiators and/or floor heating. The energy to be stored is solar or residual heat or electricity that is generated during off-peak periods or by wind energy.

A computer model for a storage system in which a gas is absorbed by a liquid absorbent was developed for the purposes of the study. System alternatives and various working pairs for the cycle were compared with the help of this model. The computer model was verified in an experimental set-up with a heat output of 5 kW.

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2 DESCRIPTION OF SYSTEM ALTERNATIVES

2.1 GENERAL

The system for storage of thermal energy by means of an absorption cycle is similar to the intermittently operating refrigerating machine, as invented by Ferdinand Carré in 1859 (Thévenot, 1979). The Carré machine (Fig. 1) consisted of two main components which were used alternately as evaporator or condenser and as absorber or desorber. In the cooling mode, gaseous ammonia was absorbed by the liquid ammonia/water mixture in the absorber, causing a pressure decrease in the system. As a consequence ammonia evaporated at a low temperature, taking heat (Qe) from the object to be cooled.

In the regenerating mode, ammonia was boiled out of the mixture in the desorber, for which heat (Qd)

was supplied at a temperature of about 130 °C. The heat of condensation (Qc) was transferred to the

environment. NH3 evaporator , i Q. • —^ A T« N H3/ H20 absorber T . Q. Td NH3 ■ condenser T. ' Q c ' B N H3/ H20 desorber Qd Fig. 1

Intermittently operating refrigeration machine of Carré. A: cooling mode.

B: Regenerating mode. C: Energy balance.

In principle such a cycle can be used for storage as well. In that case the heat of absorption (Qa), that

consists of the heat of condensation and the heat of mixing, is the output. The gaseous absorbate may be absorbed by a liquid or a solid absorbent. An example of a cycle with the latter is the absorption of gaseous methylamine (CH3NH2) in solid lithium chloride (LiCl).

As the cooling function (Qe/Qa) of the Carré cycle was low, these systems were ousted by

compressor installations. In the case of storage, however, it is the ratio Qa/Qa that is of interest. Both

condensation and mixing heat are released in the absorber. If the heat of mixing is negative (i.e. heat is produced on mixing; see subsection 3.3.3), the heat of absorption is greater than the heat of evaporation:

Q./Qd > Qe/Qd

According to the energy balance of the system over a complete cycle (see Fig. lc) is: Qe + Qd = Qc + Q.

(2.1)

(2.2)

The temperature (Te) of the gas leaving the evaporator is lower than the temperature (Tj) of the gas

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the heat (Qe) supplied to the system at a low temperature is less than the heat (Qc) transferred to the

environment:

Qc < Qc (2-3)

Hence, it follows from the energy balance of Equation (2) that:

Qa/Qd < 1 (2-4)

2.2 SOLID ABSORBENT

2.2.1 Heat production

The scheme for a storage system with a solid absorbent in the heat production (discharge) mode is presented in Figure 2a. The pressure of the pure absorbate and of the absorbate in the absorbent is shown in the In p-l/T diagram (Fig. 2b).

The liquid absorbate is evaporated during the heat production period at a temperature Te and a

pressure pe. The heat of evaporation (Qe) is taken from a low-temperature heat source (environment or

residual heat) at a temperature Thsp. The gaseous absorbate is conducted to the absorber. Solid absorbents may swell on absorbing the gas; this raises problems with respect to the construction of the heat exchanger.

The gas enters the absorber with a pressure pa. The equilibrium temperature at this pressure is Ta.

Absorption, however, needs a driving force (Apabs), and this causes subcooling (ATabs). Heat of

absorption is thus released at a real absorption temperature Tar. Furthermore, there is a temperature

drop of ATeab over the heat exchanger between the absorbent and the distribution circuit, where the heat of absorption is available at a temperature Tnet.

Should the temperature of the heat output be increased temporarily, part of the heat output (Qa > Q e )c a n be transferred back to the evaporator to increase the evaporation temperature. In this

case, however, the heat flux out of the low-temperature heat source is reduced and the net heat output is decreased.

Another way of increasing the temperature (Tnet) of the heat output is to increase the absorber

pressure by means of a booster compressor. In this case, mechanical energy has to be supplied during the heat production mode and so the storage function is decreased. Furthermore, the compressed absorbate has to be free of oil to avoid pollution of the absorber, as oil on the absorbent will increase the required driving force (subcooling) for absorption. The design of the booster compressor thus needs special provisions to meet this specification.

booster-compressor P.T. i Q . '-&-low U m p h*at BOUTC* distribution m t e r / g l y c o l r S h evaporator T.r T. -"■ 1/T Fig. 2 T° rh" T

System with solid absorbent, in heat production mode. A: Flow scheme.

B: Equilibrium vapour pressure of pure absorbate and of absorbate in absorbent, as a function of the temperature (In p vs. 1 / T diagram).

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2.2.2 Storage by means of heat (alternative I)

In the charge mode according to alternative 1, the heat of desorption is supplied by an external high-temperature heat source (e.g. solar collector or industrial residual heat) at a temperature Text

(Fig. 3). The gaseous absorbate is conducted to a condenser. The conduct pipe between desorber and condenser is equipped with a non-return valve for safety purposes and gives a pressure drop of Apcon

(Fig. 3b). The heat of condensation is transferred to the environment.

The condenser in this mode is the same component as the evaporator in the production mode. The heat of condensation in the storage mode can be used to increase the temperature of the heat source for the production mode (e.g. the soil). However, an increase in the temperature of the heat sink in the storage mode (Thss > Thsp) requires a higher desorption temperature (Td in Fig. 3b) and consequently a

higher temperature (Text) of the external heat source.

The energy balance over a complete cycle is, according to Equation (2):

Qe + Qd = Qc + Qa (2.5)

The energetic efficiency of the storage system is defined as high-grade heat output per high-grade heat input. The energetic efficiency of a complete cycle of heat production and storage by means of alternative 1 is thus, in accordance with Equation (4), less than unity:

Tl.nl = Qa/Qd < 1 (2.6)

2.2.3 Storage by means of a separate heat pump (alternative 2)

In alternative 2 the heat of condensation is not transferred to the environment but is used as heat source for a heat pump. This heat pump supplies the heat of desorption at the required temperature (Fig. 4).

The evaporator of the heat pump is combined with the condenser for the absorbate. When the heat pump is started, heat is withdrawn from the liquid absorbate still present in the condenser and the temperature in this component decreases. At continuing desorption the absorbate will condense on the evaporator of the heat pump, causing a higher evaporator temperature. The system will reach an equilibrium at temperatures such that the compression energy on the refrigerant in the heat pump (Ehp),

together with the heat of condensation of the absorbate, just equals the required heat of desorption. The transfer of heat into the solid absorbent is more difficult than the transfer out of the condensing absorbate. A system with a fine infrastructure is needed for a good exchange of heat with the absorbent. Therefore the heat output of the heat pump is transferred to the absorbent via a water circuit with forced circulation, just as in alternative 1.

< _{I )} ( * ) ( T> » ' ^ wa > C 1 beat ■ink 1 *r/«lTcol A T„, 1 high tamp. heat eource 1 rïï «.ter f Pc. Tc i « c > ( * 1 l ) In p Fig. 3

Storage by means of heat from an external high-temperature heat source (alternative 1; solid absorbent). A: Flow scheme.

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1

I". ( 1 ( refrigerant _ 1 " 1 heat pump -to— A "I r-heel fïl Ki) n U r Pd Td * « d

c^H

In p Fig. 4

Storage by means of a separate heat pump (alternative 2; solid absorbent).

A: Flow scheme. B: In p vs. 1/T diagram.

The system designed according to alternative 2 is independent of the environment during the storage mode: only mechanical energy is supplied but no heat is exchanged with the environment. Since heat (Qe) is supplied to the system in the heat production mode, the energy balance of a complete cycle is:

Ehp + Qe = Qa (2.7)

Consequently, the energetic efficiency of a complete cycle of heat production and storage by means of alternative 2 based on high-grade energy input is greater than unity:

11.02 = Qa/Ehp > 1 (2.8)

2.2.4 Storage by means of an integrated compressor (alternative 3)

In alternative 3, the absorbate is condensed at a temperature such that the heat of condensation can be used directly for the desorption. The pressure of the absorbate is increased for this purpose by a compressor to such an extent that the condensation temperature is higher than the required desorption temperature. A multi-stage compressor with intercooling can be used to avoid high compression ratios (Fig. 5).

The heat of condensation of the absorbate and the heat of compression are transferred to the desorber by means of a water circuit. As in alternative 2, the circulation in this circuit is forced by a pump. When the compressor is started, the absorbent is at ambient temperature and the suction pressure of the compressor is low. On continuing operation, the desorber temperature and pressure increase. The system will reach equilibrium at pressures such that the heat of compression (Ec), together with the heat

of condensation, equals the required heat of desorption. This alternative also involves no exchange of heat with the environment during the storage mode; only mechanical energy is supplied to the compressor. A

I""

I I 1 ( * < '

/

J / |Ec2

—A-H

v^r

/* / 1 P2 £ T ^ . /T\ - • * ' ^ i

S*-y^ PdTa | Q d ) ( ₁₎ ( ₎ In p Fig. 5

Heat storage by means of an integrated compressor (alternative 3; solid absorbent).

A: Flow scheme. B: In p vs. 1 /T diagram.

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Analogous to Equation (7), the energy balance of a complete cycle is:

Ec + Qc = Qa (2.9)

The energetic efficiency of a complete cycle of heat production and storage by means of alternative 3 based on high-grade energy input is therefore also greater than unity:

n«>3 = Qa/Ec > 1 (2.10)

In contrast to alternative 2, alternative 3 does not require a separate refrigerant circuit. On the other hand, precautions should then be taken to avoid oil pollution of the absorber because, in this alternative, the compressor is integrated in the absorbate circuit.

2.3 LIQUID ABSORBENT

2.3.1 Heat production

A disadvantage of systems with solid absorbents as described in the previous sections is the heat loss between two modes. The absorber with the total absorbent mass is at operational temperature at the end of a charge or discharge period. During the period between these two modes, the absorbent temperature decreases and the heat capacity of the absorbent causes a heat loss for the storage cycle. The application of a liquid absorbent allows the use of a scheme as shown in Figure 6. The liquid absorbent is a mixture or a solution of absorbent and absorbate. To minimize the cooling loss, this solution is stored in a vessel at a temperature Tsv that is slightly higher than the ambient temperature.

The weak solution with a mass fraction ww (absorbate/solution) is circulated from this vessel over the

absorber, where heat is produced on absorbing gas. The strong solution leaves the absorber at operation temperature. The strong solution is circulated back to the storage vessel after it has been cooled by heat transfer to the weak solution. If there is a difference in density between the weak and the strong solution, stratification in the storage vessel will prevent them from mixing. Almost the entire absorbent mass in

E

MJ)

booster compressor P . T . . q . ( f distribution -®-P . T . « -Fig. 6

System with liquid absorbent, in heat production mode.

0

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this set-up, is kept at temperature Tsv. Cooling loss is caused only by the heat capacity of the smaller

absorber.

The temperature of the produced heat is a function of the mass fraction (Fig. 7a). The temperature in the upper part of the absorber, where the weak solution enters, is Taw whereas the strong solution leaves

the absorber at the bottom with the lower temperature Tas. The mass fractions between which the

absorption takes place (ww and ws) can be chosen in such a way that the temperatures Taw and Tas meet

the needs of the distribution system, to which the heat from the absorber is exchanged in counterflow. In this case, the pressure of the evaporated absorbate (pe) does not need to be increased by the booster

compressor and the difference between the mass fractions (ws - ww) is fixed for a given evaporation

temperature (Te).

The energy density of the system depends on the specific heat of absorption and on the mass of gas that can be absorbed by a unit of absorbent. Consequently, the difference between the mass fractions (ws - ww) has to be large for a high energy density. This implies that the temperature difference over the

heat distribution system has to be as large as possible. Moreover, the difference between the mass fractions (ws - ww) can be increased for a given temperature difference by dividing the absorption into

more steps (Fig. 7b). In that case, in each step the entire content of the storage vessel is circulated over the absorber where the mass fraction is increased from wsn to wS(„+[). As the mass fraction increases at

each step while the temperatures remain constant, the absorption pressure also increases, so that the booster compressor requires more energy.

The booster compressor can be used in this scheme also to increase the temperature of the produced heat.

T. T„ T „ •- 1/T Te T>> T>ir ^ 1 / T

Fig. 7

Heat production by absorption, represented in the In p vs. 1 /T diagram. A: Absorption in one step.

B: Absorption in more steps.

2.3.2 Storage by means of heat (alternative 1)

The storage mode of a system with liquid absorbent, according to alternative 1, is shown in Figure 8. To charge the system, the strong solution is circulated from the storage vessel to the desorber, where the heat of desorption is supplied by an external heat source with a temperature Text. The desorption can be

executed in one or more steps (Fig. 8b). The pressure drop Apcon and the temperature drops over heat

exchangers are omitted in Figures 8-10 for clearness' sake.

The heat of desorption is exchanged in counterflow. At the top of the desorber where the strong solution enters, the desorption temperature is T(js. A higher desorption temperature (T(jw) is required at

the bottom, where the weak solution leaves the desorber. This weak solution is cooled by heat transfer to the strong solution before it enters the storage vessel with a temperature Tsv.

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-+0- _{In p} strong solution Pd Tda Qd

c

r?

high temp. heat ïource -©-Text desorber weak solution JSo_ -®-heat sink c o n d e n s e r

®

storage vessel Fig. 8

Storage by means of heat from an external high-temperature heat source (alternative 1; liquid absorbent). A: Flow scheme.

B: In p vs. 1 /T- diagram.

In case the vapour pressure of the absorbent is not negligible, the desorbed gas has to be rectified in order to avoid transfer of the absorbent from the desorber to the condenser. The heat of rectification is transferred to the environment. The heat of condensation of the absorbate is transferred from the condenser to a heatsink at a temperature Tc > Thss.

2.3.3 Storage by means of a separate heat pump (alternative 2)

The flow scheme of a system with liquid absorbent in the storage mode with a separate heat pump is given in Figure 9a. To charge the system, the solution is circulated over the desorber in the same way as in alternative 1. The heat of desorption is supplied by the heat pump, that uses the heat of condensation of the absorbate as a heat source. If the desorbed gas has to be rectified, the heat of rectification is also transferred to the evaporator of the heat pump.

To avoid large temperature differences in the exchange of the nearly isothermal heat output of the heat pump to the absorbent, the temperature difference of the absorbent over the desorber (Tdw -T^)

has to be small (see also Fig. 28 in section 4.4). The desorption is therefore carried out in several steps (Fig. 9b). At each step, the process reaches equilibrium at temperatures such that the heat output of the heat pump just equals the required heat of desorption.

The exchange of heat from the condenser of the heat pump to the liquid absorbent can be a direct one; there is no need for an additional water circuit as in the system with a solid absorbent.

2.3.4 Storage by means of an integrated compressor (alternative 3)

The flow scheme with alternative 3 for a system with a liquid absorbent is given in Figure 1 Oa. The heat of desorption is supplied by the heat of condensation and the heat of compression. To charge this system, the strong solution is circulated from the storage vessel to the heat exchanger where it is heated by the returning weak solution. The desorption starts in this heat exchanger. Continuing desorption takes place in the condenser where the heat of condensation of the absorbate is transferred to the strong solution. The remainder of the heat of desorption is exchanged in the desorber. For that purpose the gaseous absorbate is conducted back to the desorber after the first and second stage of compression, to exchange heat with the absorbent.

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desorber In p 1 Pc3 Pc2 Pel B + X / X / / / /_. / / w»

/ /

""

/ / / W» 2 / / / W»3 1 y \ \ ^ cl o2 c3 d» d»l dn2 dw3 l / T Fig. 9

Storage by means of a separate heat pump (alternative 2; liquid absorbent).

a - b = desorption

a—c = 1st stage compression c - d = intercooling

d - e = 2nd stage compression e - f = extraction of superheat

and condensation heat —.- =. pure absorbate

Fig. 10

Storage by means of an integrated compressor (alternative 3; liquid absorbent).

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If the desorbed gas needs to be rectified, the rectification heat is transferred to the cold strong solution, before the heat exchanger. The exchange of heat between absorbate and absorbent can be direct: again, as in alternative 2, there is no need for an additional water circuit.

To avoid a large pressure difference between condenser and desorber the desorption is divided into steps. At each step the system will reach equilibrium at pressures such that the heats of compression and condensation just equal the required heat of desorption. Desorption, divided into three steps, is shown in Figure 10b.

2.4 COMPARISON BETWEEN SYSTEMS WITH SOLID AND WITH LIQUID ABSORBENTS It appears from the previous sections that the system with a liquid absorbent has the following advantages with respect to systems with solid absorbents:

(1) the mass fraction can be chosen in such a way that the required temperature of the heat output is met;

(2) the cooling loss between the charge and discharge mode is reduced by the introduction of a storage vessel and a heat exchanger between weak and strong solution;

(3) the volume change on absorbing gas (swelling) has no consequences for the construction of the absorber;

(4) the exchange of heat from the heat pump (alternative 2) or from the absorbate (alternative 3) to the absorbent can be direct so that there is no need for an additional water circuit.

The disadvantages of the application of some liquid absorbents with respect to solid ones are: (1) some liquid absorbents can demand rectification of the desorbed gas;

(2) the temperature difference over the heat distribution system has to be as large as possible for a high energy density of the storage system.

Because of the features mentioned above, the possibilities will be investigated of thermal storage by means of an absorption cycle in which gas is absorbed into a liquid absorbent.

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3 THERMODYMICS OF THE ABSORPTION CYCLE

3.1 GENERAL

The storage of thermal energy by means of an absorption cycle with a liquid absorbent was described in section 2.3. A computer model for such a cycle will be given in chapter 4. For this purpose, the physical data of the working pairs are needed. The required thermodynamic relations are the equilibrium pressure, the enthalpy and the volume of the mixtures as a function of temperature, pressure and composition:

ps = fp(T,w) (3.1)

h = fh(T,p,w) (3.2)

and

v = fv(T,p,w) (3.3)

The thermodynamic behaviour of mixtures and solutions is commonly described by means of the Gibbs energy (or free enthalpy). This is an extensive thermodynamic property of state, defined as:

G = H - T S (3.4) If the Gibbs energy is known as a function of temperature, pressure and composition, all other

thermodynamic functions can be derived, so that the Gibbs energy can be used as a fundamental property. For an ideal mixture it can be calculated from the data for the pure components. The difference between the Gibbs energy of a real mixture and that of an ideal one is the excess Gibbs energy that has to be derived from measurements. This excess value can be described by coefficients as was done by, for instance, Schulz (1971) for NH3/H20, Michels (1977) for H20/LiBr and ledema (1984)

for a mixture of lithium bromide and zinc bromide in methanol: LiBr-ZnBr2/CH3OH. These authors

used 16, 24 and 64 coefficients, respectively.

However, a simplified description by means of a small number of coefficients is needed to make a selection out of many potential working pairs. This simple description does not require high accuracy. Furthermore, it is only useful to use a large number of coefficients if many reliable values are available. The number of published measurements is however very limited.

Potential working pairs are mixtures of liquids or solutions of solid substances in a solvent. A thermodynamic description of mixtures and solutions is given in a KEMA publication (Ruiter, 1986). In order to simplify this description the following assumptions are made:

(a) the vapour pressure of the absorbent is negligible compared to the vapour pressure of the absorbate; (b) in correlating the vapour pressure as a function of temperature and composition, the ratio of the

fugacities is supposed to be equal to the ratio between the saturation pressure of the pure absorbate and that of the absorbate in the mixture;

(c) a solution of a solid substance in a solvent is regarded as a mixture of a subcooled liquid and the solvent;

(d) the electric interactions in concentrated (w > 0.20 kg.kg-1) electrolyte solutions are not considered;

(e) the enthalpy of liquid and solid substances is independent of the pressure; (f) the excess value of the Gibbs energy is independent of the pressure; (g) the heat of fusion is independent of temperature and pressure;

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(h) the change of volume on fusing is negligible;

(i) dissociation of the components in a solution is independent of temperature, pressure and composition.

A survey of the thermodynamic relations, as quoted from Ruiter (1986), is given in Tables 1 and 2.

Table 1

Survey of the required thermodynamic relations for pure components (Ruiter, 1986).

C>-<ï^-T](0)^

r

f.)

Table 2

Survey of the required thermodynamic relations for mixtures and solutions (Ruiter, 1986).

x w M ^ k ( l - w ) + w MA

u

B

< = G<

m +

(.-X)(<§p)

Tp ƒ (VB8 - VB' )dP = uB + RT In ( j | ) + f (VBg - V& )dp PsB RTlnaB = uB + R T l n X PsB H - G - T ( M ) P X Mm= ( l - X )I^A+ X MB

H

d B

= H'

m +

(.-X)(ff)

Tp h d B " MB^ h = (l-w)h^ + whB'+ J j Mm h = (i - w) (h;s + *fr\) + whB' + |j=-v - ( l - wXv J + V ^ + w v J+ i ( ^ ) T , x (a) (b) (c) (d) (e) (0 (g) (h) (i) Ü) (1) (m) mixtures solutions

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3.2 PURE COMPONENTS

3.2.1 Equilibrium pressure

In the above mentioned Kema publication (Ruiter, 1986), also approximation series have been published for the thermodynamic quantities. The relation between the equilibrium pressure and the temperature of a pure substance (denoted by *) can be approximated by a series based on the equation of Clapeyron, extended by Rankine and Nernst. It is assumed that a series with three terms is sufficient for the simple description. The equilibrium pressure (p?) of a pure component i is then approximated by:

aps + ^ + CpslnT (3.5)

In (&) = VPrcf/

in which the reference pressure pref = 1 kPa. The coefficients aps, bps and cps have to be derived from

literature data.

3.2.2. Enthalpy

3.2.2.1 Liquid or solid phase

The specific enthalpy of liquid or solid pure component i, at temperature T and pressure p, is:

% = h ^ , + (hftp) - hfoPo)) (3.6)

in which the reference value at temperature T0 and pressure p0 in the respective aggregation state, is

chosen to be:

h'&Po) = 0 (3.7) Neglecting the pressure dependence of the enthalpy for liquids and solids (assumption e), the change in

enthalpy between T,p and T0p0 is, according to Eq. (b) of Table 1:

h ^ , p ) - h , ^o P o )= r ï c ^ d T l (3.8)

The specific heat capacity of the liquid or solid component i is approximated by a power series of the temperature as:

Cpl's = a^ + b^T + ccpiT2 (3.9)

The specific enthalpy of the liquid or solid pure component i at a temperature T, a pressure p and in the same aggregation state as the reference condition, is then, from Equations (6)-(9):

bftrt = M T - T0) + èb^CT - ID + èccpi(T3 - T?) (3.10)

3.2.2.2 Gas phase

Because the vapour pressure of the absorbent is neglected (assumption a), the gas above the mixture can be considered as pure absorbate (denoted by B). The enthalpy of the gaseous absorbate, at temperature T and pressure p, is:

hj#r,p) = hB(ToPo) + Aeh^roPo) + (h&,p) - ihfcjj) (3.11)

in which hB(ToPo) is the enthalpy of the liquid pure absorbate at T0 and p0. The heat of evaporation in

this state is AehB(ToPo)- As, according to Equations (6) and (11), the enthalpy of the gas phase and the

liquid phase are related to the same reference state (T0,p0), the reference pressure cannot be chosen

freely but po has to be the saturation pressure at temperature T0.

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**■*»-!, = [?4dT]

H +

[ J [vê-T(^)J

dp

]

i

(3.12) The simplified description has been made by the virial equation of state, using the second virial coefficient (B) only:

v

B

»

= S ! =

^ ( l

+

Bp)

(3.13)

MB MBp

in which Vfjg and Vjjg are the specific and the molar gaseous volume respectively, and MB is the molar

mass of the absorbate. The virial coefficient is approximated by a power series of the temperature with negative exponents, as:

R \T T2 + V)

Substitution of B in Equation (13) yields: R T b„ c, 4- a -I—8 4—i -~ "g -~ f -~ J2 (3.14) (3.15) (3.16) B ~ " MB P

The specific heat capacity at constant pressure is, according to Equation (a) of Table 1:

**• » - * . - T { ( $ F )**

F

« P

in which the specific heat capacity at infinite low pressure is approximated by a power series of the temperature:

c;io = a ^ + b ^ T + ccpgT2 (3.17)

Combination of Equation (12) with Equations (15)-(17) gives the specific enthalpy change as: AhB* = hBfr2P2) - hïfop,, = acpg(T2 - T.) + ib^(T22 - T,2) + iccpg(T23 - V) + 2bgp,(^- ~ ^ ) +

/ 1 1 \ , 2b. 3c„., . ,, . . . + topt^-Y?) + (ag + "TT_g_T,1 + X2 )Ö»2 " Pi) (3-18) Table 3 Approximation series. quantity specific heat equation of state equilibrium pressure excess value of Gibbs energy component absorbent absorbate absorbate absorbate absorbate mixture phase liquid liquid gas gas liquid/ gas liquid approximation cpA = acpA + bcpA T + CcpA T CpB.= acpB + bcpeT + ccpBT2 cp-0 = acpg + "cpgT + ccpgT „ RT b. c„ V^ = MB- p+ a«+f + # Ps'i = exp(aps + ^ + cpslnT) ■ . Gem =X(1-X)[A0 + A,(2X-1)] A0 = aT + b + c/T A, = d T + e + f/T dimension kJ.kg-'.K-1 kJ.kg-'.K"1 kJ.kg-'.K-' m3.kg"' kPa kJ.kmol"1

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3.2.3 Entropy

The gaseous absorbate is compressed in the storage mode as well as in the heat production mode. To be

able to calculate the work of compression, the change in entropy has to be known.

According to Equation (c) of Table 1, the change in entropy between two states (Tipj and T2P2) of

the gaseous absorbate is:

* * > - * , „ > = [ J ^ T ] - [ ƒ ( * £ ) dp] (3.19)

Combination of Equations (15)-(17) with Equation (19) gives the change in specific entropy between

two states as:

A%* = s^r

2P2

, - SB

g

fr

1P1

) = a^ In (^J + b^C^ - T,) + i c^Ol - Tf) + b

g

p, ^ - ^ J +

V 2<(£-£) - £ * < £ ) + ( | + § ) < * - * ) (3.20)*

The approximation series are summarized in Table 3. The coefficients for these series are given in

Tables 4 and 5.

3.3 MIXTURES

3.3.1 Composition

The working pairs of absorbate and absorbent to be considered in this investigation consist of binary or

ternary mixtures or solutions. In case of a ternary one, the absorbent is itself a solution with a fixed

composition. Thus, the composition of a working pair consisting of n^ moles of absorbent and ne moles

of absorbate can be described by the mole fraction (X) or the mass fraction (w) of the liquid absorbate:

X = X'

B

= "

B

(3.21)

n

A

+ n

B

and

w = w„

(3.22)

The relation between the mole and mass fraction is given by Equation (a) of Table 2:

X =

M

B

k

n W

, <

3

'

23)

-^-(l-w)

+

w

The factor (k) is equal to the number of moles of particles that are formed when one mole of absorbent

is dissolved; this factor is a function of the degree of dissociation (Ruiter, 1986: Eq. 200). The

dissociation will generally be a function of temperature, pressure and composition. For this simplified

description, however, k is supposed to be constant (assumption i). If no dissociation occurs, this

constant k = 1.

3.3.2 Equilibrium pressure

The equilibrium pressure (p

s

) of a mixture follows from Equation (c) of Table 2:

? (V

Bg

- V

B

')dp = u

B

< + RT In ( § ) + ƒ (V

B

* - V|) dp (3.24)

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in which p% is the equilibrium pressure of the pure absorbate at the same temperature as the mixture; V]88and VB' are, respectively, the molar gaseous and molar liquid volume of the pure absorbate and V|

is the molar gaseous volume of the absorbate in the mixture. Furthermore, the chemical potential of the absorbate in the real mixture is defined as the partial molar Gibbs energy:

MB

/ 5 G X V dnB /T,P,nA

(3.25)

and fjl is the excess value with respect to the chemical potential of the absorbate in an ideal mixture. The excess value of the molar Gibbs energy is approximated by the Redlich and Kister series (Redlich & Kister, 1948; Ruiter, 1986) with two terms:

Gem = X(l-X)[Ao + A,(2X-l)] (3.26)

in which in general the coefficients A0 and Aj are functions of temperature and pressure. The excess

chemical potential is, according to Equation (b) of Table 2 (also see Fig. 11): HCB = G'm + (1

**-*>(t),**

(

Application of Equation (27) to Equation (26) results in: Hl = (l-X)2[A0 + (4X-1)A1]

(3.27)

(3.28) As the vapour pressure of the absorbent is negligible with respect to the vapour pressure of the absorbate, the gaseous mixture can be considered as pure gaseous absorbate, so that:

X | = 1 and

v | =

v

B

*

(3.29)

(3Ï30) Substitution of Equations (21), (29) and (30) in Equation (24), in combination with Equation (d) of Table 2, yields:

Ps

ƒ (VB8-VB')dp = u| + RT In X = RT In aB (3.31)

PsB

where as is the relative activity of the absorbate in the mixture. It follows from Equations (28) and (31) that:

Xexp | ( 1 - X )2

RT [A0 + ( 4 X - 1 ) A

■>}

(3.32) Substitution of the molar volume VB8 according to Equations (13) and (15) in Equation (31) gives:

£ = aBe x p [ ( { ^ | dP) - ^ ( ag + ^ + ^ ) (P s-P;B) ] (3.33)

Fig. 11

Relation between excess values of Gibbs energy and chemical potential. 1 arctg 1 \ 9x ^ — /

<C

T,P L — fs

N

. 1

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Combination of Equations (32) and (33) yields:

4 = X exp { {±~£ [A. + (4X - 1)A,] - ^ (ag + ^ + ^ - vB')(p5 - P;B)} (3.34)

in which the specific liquid volume of the pure absorbate (VB') is assumed to be independent of the pressure.

Furthermore, the ratio between the fugacities of the absorbate in the mixture and of the pure absorbate at the same temperature is according to Equation (e) of Table 2:

Ps v < 1

■ff = aBe x p

In

[Ï2H

PsB

.(3.35)

If the deviation from unity of the exponential factor is neglected and it is assumed that the ratio of the fugacities can be considered to be equal to the ratio of the saturation pressure of the pure absorbate (P*B) and the pressure (PB) of the absorbate in the mixture (assumption b) it follows from Equation (35) that:

. P B

PsB = a„ (3.36)

As the vapour pressure of the absorbent is neglected, the pressure (PB) of the absorbate is equal to the equilibrium pressure (ps) of the mixture. Substitution of as according to Equations (32) and (36) gives a

simplified relation for the correlation of the equilibrium pressure (ps) as a function of the mole fraction

(X):

pB = Ps = Ps*BXexp

| ( 1 - X )

2

RT

[A. + (4X

- DA,]}

(3.37)

in which the equilibrium pressure of the pure absorbate at temperature T results from Equation (5): p;„ = pr e f exp (a„s + - ^ + Cp, In T) (3.38)

3.3.3 Enthalpy

The enthalpy of a mixture is equal to the sum of the contributions (h*) of the pure components and the heat of mixing, all at the same temperature and pressure as the mixture. The heat of mixing is the excess value (he) of the enthalpy of a real mixture compared to the enthalpy of an ideal mixture (Fig. 12a). If

on mixing heat is produced (this means that heat has to be removed out of the system to keep the temperature and pressure constant), the excess value is negative. According to Equation (j) of Table 2,

A

real mixture

/ i d a a l mirtum

real solution

Fig. 12

Enthalpy of mixtures and solutions. A: Mixture.

' « T . p )

o h*<Vo>

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the specific enthalpy of the liquid mixture at temperature T and pressure p, is:

h(T,p) = (1 - w) h ^ p ) + w h^.p) + h^p) (3.39)

The specific excess enthalpy is:

* = ^ (3-40)

in which, according to Equation (g) of Table 2, the molar mass of the mixture is:

M

m

= ( l - X ) - ^ + XM

B

(3.41)

According to the Gibbs-Helmholtz relation (Eq. (0 of Table 2) the molar excess enthalpy is:

H

L = G

- T ( ^ )

p x

(3.42)

Substitution of G^, according to Equation (26) in Equation (42) yields:

Hi . X(. - X) { A. - T ( £ )

f

+ (2X - I) [A, - T ( « £ ) J } (3.43)

In a first approximation the heat of mixing is independent of temperature and pressure. In this case, the

following has to apply in Equation (43):

and

U

A

'-

T

(w)}=° w>

Solution of the differential Equations (44)-(47) results in:

A

c

= aT + b (3.48)

and

A, = dT + e (3.49)

In order to allow corrections to be applied for a possible temperature dependence of the heat of mixing,

these equations are extended into:

A

0

= aT + b + c/T (3.50)

and

A, = dT + e + f/T (3.51)

By substitution of A

0

and A! according to Equations (50) and (51) in Equations (46) and (47), it

follows that:

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r

P

('40-° <

3 ">

As this has to apply for each temperature, is:

dp dp ~~ dp dp ~~

According to Schulz (1971), the pressure dependence of the excess value of the Gibbs energy for the ammonia/water mixture is minute. It is therefore assumed for the simplified description that a and d are also constant (assumption

f)-The relative activity then follows from Equations (32), (50) and (51) as:

aB = X exp { ^ = ^ [ ( a j + bp + *) + (4X - l)(dpT + ep + | ) ] } (3.55)

where the coefficients ap to fp are derived from known values for the equilibrium pressure and

temperatures (In p -1/T diagram; see subsection 3.5.3.1).

The molar heat of mixing follows from Equations (43), (50) and (51):

H^ = X(l - X)[(b + y ) + (2X - l)(e + | ) ] (3.56) or H^ = X(l - X ) [ ( ah + ^ ) + X(c + ^ ) ] (3.57) where: ah = b - e (3.58) bh = 2(c - 0 (3.59) ch = 2e (3.60) dh = 4f (3.61)

If the equilibrium pressures were known exactly and could be described more exactly, the constants A0

and A[ in Equations (32) and (43) should be identical. Therefore, the following should apply for thermodynamic consistency:

(3.62) (3.63) (3.64)

(3.65) However, calculation of the heat of mixing from the In p - 1/T diagram gives results that are far from exact. This method is rejected in the literature (Ando & Takeshita, 1984; Rowlinson, 1984) because it can lead to large errors. Therefore, the coefficients ah to dh as given in Table 7 are derived as far as possible from known values of the molar heat of mixing.

The specific enthalpy of the liquid mixture at temperature T and pressure p follows from Equations (10) and (39) as:

hfr.P, = (1 - w)[acpA(T - T0) + ib^CT2 - TJ) + i Cq)A(T3 - T*)] + w[acpB(T - T0) + i b ^ T2 - TJ) +

+ *ccpB(T3-Tg)] + h< (3.66) ah = bh = ch = and dh = bP -2(cp 2ep 4fP eP -fP)

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in which, according to Equations (40), (41) and (57), the specific excess enthalpy is:

X(l-X)[(a

h

+ ^ ) + X(c

h

+ ! ) ]

h< = t ^ j - ^ - (3.67) ( l - X J - ^ + X M ,

According to Equation (h) of Table 2 the partial molar heat of mixing of the absorbate is:

HdB = H^ + ( l - X ) ( ^ ) T p (3.68)

The specific partial heat of mixing of the absorbate follows from Equation (i) of Table 2 and from Equations (57) and (68):

3.3.4 Volume

As in the case of enthalpy, the volume of a mixture is also equal to the sum of the contributions (V*1) of

the pure components and of the excess value of the volume. According to Equation (k) of Table 2 the specific volume of a mixture is:

v - ( l - w ) ^ + w ^ + ] i - ( ^ )T x (3.70)

in which vA' and VB' are the specific volumes of the pure absorbent and of the pure absorbate, at the

same temperature and pressure as the mixture. As the excess value of the Gibbs energy is assumed to be independent of the pressure (assumption 0» Equation (70) is reduced to:

v1 = ( i _w) v ;1 +WVÏ (3.71)

3.4 SOLUTIONS

A solution of a solid substance (A) in a solvent (B) is considered as a mixture of the solvent and a subcooled liquid (assumption c). When the solid component is dissolved in the solvent, the heat h] is absorbed. This heat includes the heat of fusion (Afh^) of the solute (A). The excess enthalpy of the solution with respect to an ideal mixture is (Fig. 12b):

h' = h f - ( l - w ) Afh ; (3.72)

The solution has a limited composition range. When the concentration of solute (A) is increased, it becomes saturated. If more substance (A) is added than corresponds with the saturation composition (Wsa,), the surplus of A is not dissolved.

According to Equation (39) the specific enthalpy of the mixture at temperature T and pressure p is:

h(T,p) = (l-w)h;( T,p ) + w h^iP) + hfr,p) (3.73)

in which IIA is the enthalpy of the pure component (A) in a Active state, defined by the same temperature, pressure and aggregation state as the mixture. In reality, component (A) is a solid substance under these conditions. Assuming, however, that the heat of fusion is independent of temperature and pressure (assumption g), component A can be considered as a subcooled liquid with an enthalpy (Fig. 12b):

hAfr,p) = hAcrj» + Afh; (3.74) in which hAS is the enthalpy of the solid substance (A). Combination of Equations (73) and (74) gives

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Equation (1) of Table 2:

V , ) = (1 - wXhVp) + A&) + w hB'cr.p) + rfrp) (3.75)

By choosing the reference enthalpies for component A and B respectively as:

h;V„P„> = h^oPo) = 0 (3.76)

the enthalpies IIAS and he' in Equation (75) can be substituted according to Equation (10). This

substitution gives the enthalpy of the solution at temperature T and pressure p, as:

V.P) = 0 " w) [a^CT - T0) + è b ^ T2 _ To2) + $ CcpA(T3 - T03) + A ^ + w [acpB(T - T0) +

+ * M T2 - T02) + } CcpB(T3 - T03)] + h' (3.77)

in which the specific excess enthalpy is given in Equation (67).

The specific volume of a solution can be derived in analogy to Equation (75) as (see Eq. (m) of Table 2):

v1 = (1 - w)(vl8 + AfV;) + w vB' + V (3.78)

in which the excess volume, according to assumption f, is:

* = - L ( ^ ) = 0 (3.79) Furthermore, the change of volume on fusing is supposed to be negligible (assumption h) so that the

specific volume of a solution is:

v1 = ( l - w ) v ;s + wvB' (3.80)

3.5 CALCULATION OF THE COEFFICIENTS

3.5.1 General

The coefficients of the approximation series, as given in Table 3, are derived from published data. For the pure absorbate, these coefficents have to apply for the temperature range:

2 6 0 K < T < 4 5 0 K (3.81) The domain for which the constants for the mixtures and solutions have to be valid is defined by the

temperature range:

290 K < T < 380 K (3.82) and by the range of the mass fraction:

0.20 kg.kg-' < w <, 1.00 kg.kg-' (3.83) Because for some mixtures the need for rectification increases at lower absorbate mass fractions,

desorption is not extended to lower values but is stopped at an arbitrarily chosen minimum of about w = 0.20 kg.kg-1.

3.5.2 Pure components

The coefficients for the specific heat capacities of solids, liquids and gases can be calculated according to Equations (9) and (17) from at least three known values of the heat capacities at three different temperatures. The equilibrium pressure and the specific volume of the gas have to be known for at least three different temperatures, in order to calculate the coefficients according to Equations (5) and (15). The coefficients for the pure components, as calculated from published data, are given in Tables 4 and 5.

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Table 4

Coefficients for the absorbate.

compo- equilibrium pressure nent B

specific heat capacity equation of state

liquid/gas liquid: cpB gas: c -• 0 liquid gas:' molar

mass heat of evapora tion source (0°C) \h* K U.kg-'.K"1 kJ.kg-'.K"2 kJ.kg"'.K 3 kJ.kg"'.K"' kJ.kg."'.K_2 kJ.kg'.K- 3 m'.kg-' m3.kg~' m'.K.kg-' m3.K2.kg~' kg.kmol"' kJ.kg"1

0 0 _NHR22 -O.3647OE0 -0.16682E4 ₃_{0.I5835E2 -0.27042E4} CH3NH2 0.33853E2 -0.38375E4

R123' 0.34726E2 -0.41567E4 CH3OH 0.45746E2 -0.58608E4

TFE 0.17528E2 -0.49879E4

H20 0.47613E2 -0.6S635E4

0.22660E1 0.2588E2 -0.1628E0 0.2683E-3 0.2407E0 0.1540E-2 -0.6169E-6 0.843E-3 -0.4573E-2 0.4266E1 -0.1308E4 86.47 204.9 0.26414E-I 0.3470E2 -O.2026E0 0.3408E-3 O.I959EI -0.5000E-3 0.3125E-5 0.167E-2 -0.2617E-1 0.224OE2 -0.5838E4 17.03 1260.7 -0.26494E1 0.3075E1 0.3031E-2 -0.8889E-5 0.50O9E0 0.4231E-2 -0.1145E-5 0.152E-2 -0.3656E-1 0.3I31E2 -0.7129E4 31.06 825.2

-0.28680E1 0.1009E1 -0.2040E-2 0.6667E-5 0.1864E0 0.1943E-2 -0.1127E-5 0.675E-3 0.0* 0 . 0 ' 0.0* 152.93 190.0 -0.40846E1 0.4079E1 -O.1650E-I 0.3833E-4 0.1209E1 -0.9457E-4 0.2104E-5 0.124E-2 -0.7453E0 0.5851E3 -0.1172E6 32.04 1179.0

0.25360EO-0.1036EI 0.I270E-1 -0.1158E-4 0.1396E0 0.3050E-2 -0.1563E-5 0.719E-3 -0.3344E-1 0.1258E2 -0.1431E4 100.04 449.0 -O.42890E1 0.5331EI -0.7297E-2 0.I157E-4 0.1808E1 -0.1063E-5 0.5938E-6 0.100E-2 -0.2896E-0 0.2531E3 -0.5409E5 18.02 2501.6

DKV, 1981 DKV.1981

Plank, 1953; Landolt-Börnstein, 1961,1967: VDI, 1984

Beilstein, 1972; Bokelmann & Ehmke, 1984; Weast, 1985-1986

Beilstein, 1972; DKV, 1981; Eichholzetal., 1981 Weast, 1985-1986

Bokelmann & Ehmke, 1984; Jadot (Mons), pers. comm. (1985-11-06)

Schmidt, 1969 * estimated values.

(34)

Table 5

Coefficients for the absorbent.

component A H20 H20-LiBr W:40%H2O DTG DTrG DEGDME NMP C2H602 H2S04 NaSCN LiSCN LiN03 H20-LiN03 W:25%H20 LiBr ZnBr2 LiBr-ZnBr2 mol 2:1 NaOH

specific heat capacity ck(kJ.kg-' acpA kJ.kg-'.K"1 0.533E1 -0.152E1 0.248E1 O.202E1 0.345E1 0.147E1 0.153E1 0.604E0 0.992E0 0.100E1* 0.557E0 0.800EO 0.480E0 0.232E0 0.344E0 0.592E0 .It"') bcpA k J . k g - ' . K- 2 -0.730E-2 0.187E-1 -0.370E-2 -0.676E-3 -0.972E-2 -0.766E-3 0.144E-2 0.367E-2 O.'OOOEO 0.000E0 0.219E-2 0.550E-2 0.295E-3 0.193E-4 0.12OE-3 0.433E-2 ccpA kJ.kg-'.K-3 0.116E-4 -0.250E-4 0.719E-5 0.298E-5 0.172E-4 0.542E-5 0.531E-5 -0.315E-5 0.000E0 0.000E0 0.000E0 -0.556E-5 -0.500E-7 0.000E0 0.000E0 -0.444E-5 specific volume v* m3.kg-' 0.100E-2 0.585E-3 0.991E-3 0.102E-2 0.106E-2 0.969E-3 0.902E-3 0.S43E-3 0.700E-3 0.750E-3 0.420E-3 0.566E-3 0.289E-3 0.238E-3 0.260E-3 0.469E-3 molar mass MA kg.kmor' 18.02 34.36 222.28 178.23 134.18 99.13 62.07 98.08 81.07 65.02 68.94 40.40 86.85 225.19 132.96 40.00 heat of fusion A,h 1 kJ.kg"1 _ -— -229.8 200* 367.5 275.6 203.3 74.0 130.3 170.4 source Schmidt, 1969 RadermacherA Alefeld, 1982

Bokelmann & Ehmke, 1984 Bokelmann & Ehmke, 1984 Merck & Co., 1983; Ando & Takes-hita, 1984

Bokelmann & Ehmke, 1984 DKV, 1981;Weast, 1985-1986 USDC, 1971;Weast, 1985-1986 Blytas & Daniels, 1962; Perry & Chilton, 1973

Macrissetal., 1970

Perry & Chilton, 1973; Weast, 1985-1986

Infante Ferreira, 1981 **

USDC, 1971; Weast, 1985-1986 Hütte, 1967Uemura, 1973; Weast, 1985-1986

**

Murch & Giauque, 1962; USDC, 1971; Weast, 1985-1986

* = estimated values; ** = calculated values.

3.5.3 Mixtures and solutions

3.5.3.1 Equilibrium pressure

The coefficients in the expression for the relative activity in Equation (55) are derived from known values for the vapour/liquid equilibrium pressure as a function of the temperature and composition (In p - 1/T diagram). According to Equation (34), the theoretical equilibrium pressure is:

p5th = P;B X exp { ^ = | ^ [ A0 + (4X - 1) A,] - ^ (ag + ^ + | * - vB') (p5th - P;B) } (3.84)

If this equation is to be used for the correlation of ps as a function of X, much iterative computation is

needed. This equation is therefore simplified for correlation purposes by applying assumption b. It follows from Equations (36) and (37) that the calculated equilibrium pressure is:

Pscaic = PS'B aB = PIB X exp { ^ = ^ [A0 + (4X - 1)A,]} (3.85)

Substitution of the relative activity according to Equation (55) yields:

Thermal energy storage by means of an absorption cycle

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